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Only a limited number of research has examined preservice preschool teachers' attitudes toward and beliefs about teaching mathematics, likely because there are no instruments aimed at preschool settings that have appropriately established psychometric properties. In the current study, we addressed this deficit and aimed to adapt the Preschool Teacher Attitudes and Beliefs toward Science (P-TABS) instrument in a sample of 164 Greek preservice preschool teachers and test its validity and reliability. Using a version of the P-TABS that had been adapted to mathematics, we investigated participants' beliefs about and attitudes toward teaching mathematics and the impact of their previous experiences with mathematics, as well as their math anxiety, on their beliefs about and attitudes toward mathematics teaching. The results showed that this adapted version of the P-TABS was valid and reliable, and therefore it can be useful in the assessment of preservice preschool teachers' beliefs about and attitudes toward teaching mathematics. The results also showed that teachers' math anxiety and their previous experience with mathematics explained their beliefs about and attitudes toward teaching mathematics. This suggests that introducing courses on mathematics into teacher education programs could have a positive effect on preservice teachers' beliefs about teaching mathematics.

The reference contexts that accompany the "realistic" problems chosen for teaching mathematical concepts in the first school grades play a major educational role. However, choosing "realistic" problems in teaching is a complex process that must take into account various pedagogical, sociological and psychological parameters. This paper presents a selection of problems from the new mathematics textbook of the 2nd grade of Greek primary school which were solved and commented upon by 27 postgraduate students. The results of our research showed that the empirical reference contexts put forward in these problems create many difficulties in their "deciphering", which leads us to conclude that their pedagogical role is problematic.

The study of pupils' representations of physics concepts and phenomena constitutes a central part of Science Education research, as they play a decisive role in teaching. In the study presented here, we investigate 212 fifth grade pupils' mental representations of the formation of shadows, before they were taught about it in school. The empirical data was gathered through an interview using four tasks which involved the evaluation of hypothetical situations. The research data included representations that cause difficulty in the comprehension of the position of a light source in relevance to the shadow.

This article presents a case study that examines the level of integration of mathematical knowledge in physics problem solving among first grade students of upper secondary school. We explore the ways in which two specific students utilize their knowledge and we attempt to identify the epistemological framings they refer to while solving a physics problem. Participant observation was used for data collection, and the students' verbal interactions were video-recorded. The analysis shows that they tend to use a wide spectrum of epistemological framings that entangle mathematics and physics but at the same time face significant practical difficulties in modulating the two subjects.

Our research programme, a part of which is presented in this paper, looked at four year old children's ability to use manipulatives in the construction of cube models. We looked at how pre-school children managed the creation of cube nets as a mathematical problem and whether graphical representations of solutions could become a useful tool in a child's quest for solving the nets of a cube mathematical problem. We followed the work of twenty four-year old children who were asked to solve a cube creation geometry mathematical problem. In order for the problem to be successfully solved, graphical representations of solutions had to be developed. The data analysis showed that, during the course of the programme, children developed the ability to use manipulatives in order to solve the mathematical problem. The development of strategies for graphically representing the solutions also seemed to have played an important role in solving the specific mathematical problem. [Corresponding Author: Konstantinos Zacharos]

Do early childhood education children comprehend photographs as spatial representations and are they able to use them to obtain information about space? Can they identify the location where the shooting was done? Can they use photographs to identify the positions where objects are located? These are the research questions that this article aims to investigate making a first qualitative approach. The photographs used during the research depicting a long hallway at the children's preschool, taken from two different angles. The research sample consisted of 18 children aged four- to six-years-old attending a Greek public preschool. The individual interviews with the children highlighted their ability to use photographs as sources of information about space. More specifically, the children of the sample identified from the photographs spaces known to them, and some of them were able to identify their location in the photographs and the location from where the photographs were taken. Finally, a smaller number of children were able to use photographs as a 'map' to track objects in a real space.

The purpose of this paper is to contribute to development of research tools for observation and analysis of educational practices used by teachers in preschool classrooms. More specifically, we approached the implemented curriculum of mathematics in Greek preschool education. We analysed the recorded data from a week of teaching practices in eight classrooms of Greek public kindergartens, based on Bernstein's theoretical framework on pedagogic discourse. The results showed that the actual educational practices in the observed classrooms deviated from the objectives of the official new cross-thematic curriculum for teaching mathematics in Greek kindergarten in terms of the form of transmitted mathematical knowledge, the instructional rules and strategies that teachers adopted for teaching mathematics, and the teaching-interactive relationships between preschool teachers and students.

The teaching of Probability Theory constitutes a new trend in mathematics education internationally. The purpose of this research project was to explore the degree to which preschoolers understand key concepts of probabilistic thinking, such as sample space, the probability of an event and probability comparisons. At the same time, we evaluated an educational programme which aimed to introduce children to the basic principles of Probability Theory. The research sample consisted of 29 preschoolers (with an average age of 5 years and 4 months) from two classes of a Greek public kindergarten. The research was based on a semi-experimental, three-phase plan: the pretest, the teaching intervention and the post-test. The pretest explored the children's conception of key probabilistic constructs and contributed to the planning of the teaching intervention. Through the post-test, we evaluated the contribution of the teaching intervention. The findings showed that pupils displayed a satisfactory level of comprehension of key probabilistic concepts and that, moreover, teaching this subject can improve their comprehension.

Could problem solving be the object of teaching in early education? Could appropriate teaching interventions develop to scaffold children's efforts to solve problems? These were the central questions of this article. The sample consisted of 18 children attending public pre-school in Cyprus. The problem they were asked to solve was to find all solutions of the pentomino. The children's problem solving was supported by graphically representing their solutions on squared paper. The findings show that children responded positively to the problem and were successful in finding all solutions for the specific problem. The graphical representation of the solutions and the forms of teacher-children and children-children interactions played an important role in the positive outcome of the activity. (Contains 1 table and 3 figures.)

The purpose of this paper is to critically examine the changes that took place in school mathematics knowledge for pupils aged six and seven (first grade of Greek elementary school) and its pedagogical approach, which took shape following the reforms of the mathematics curricula in 1982 and 2003. Our analysis is based on Bernstein's theoretical framework on pedagogic discourse and Dowling's theoretical framework on textual domains. The results showed that there are differences between the 1982 and 2003 reforms, in terms both of the content of mathematics knowledge, as well as of the forms of pedagogic interaction between the teacher and the pupil. (Contains 2 notes, 3 tables, and 3 figures.)

In this study we attempted to highlight the pedagogical role of activities to familiarize pre-schoolers with the measurement processes of container capacity. The sample of the study consisted of 20 subjects aged five-six, all coming from two Greek state kindergartens of the same area, bearing the same middle socioeconomic background. The research was conducted in three phases (pre-test, teaching intervention and post-test). During the pre-test and post-test, the subjects' reasoning was recorded through personal interviews, each of which lasted 15-20 minutes. In the pre-test we attempted to check whether the children could carry out direct (using just the containers) and indirect (using a common measure) comparisons between container capacity. In the teaching intervention we proposed activities to small groups of children which aimed at creating the kinds of frameworks that would allow them to compare the capacity of containers and to elaborate on the concept of capacity. Finally, in the post-test, we evaluated the influence of the teaching intervention on the improvement of the children's ability to handle issues related to the comparison of the capacity of containers, as well as to the measurement of capacity. Our findings highlight the important role of the communication framework in teaching, as it reinforces the pupils' autonomy and contributes to the acquisition of new knowledge. (Contains 2 tables.)

The questions this paper attempts to answer are related to the attitudes of student teachers of the Department of Early Childhood Education at the University of Patras (Greece) towards mathematics, as well as their views on the instruction of mathematics in Early Childhood Education. The research sample included 52 students in the fourth semester of studies, who were invited to answer a questionnaire with respect to mathematics and its instruction. The findings reveal the negative attitude our research subjects adopt towards mathematics. Their epistemological views on mathematics and its instruction do not constitute a single and solid conceptual system. These findings underline the need to improve the mathematical education offered to student teachers of Early Childhood Education. (Contains 2 tables and 1 figure.)

The present research was carried out with the participation of 106 students in their last grade in Elementary School and revealed certain problems that these students faced in understanding the concept of area measurement. The students in the sample persisted on using measurement strategies that often led to failure. Our research plan comprises a comparison between the strategies for area measurement strategies used by two groups: the experimental group (E.G.) and the control group (C.G.). The experimental group attended a special teaching course, which stressed the conceptual characteristics of the area measurement process. The present research aims at revealing the students' understanding, strategies, and misconceptions regarding area measurement. In addition to that, we examine whether the special teaching course and the use of different measurement tools may lead the two research groups to adopt different measurement strategies. (Contains 9 figures and 4 tables.)